Public Health Impact of Paxlovid as Treatment for COVID-19, United States

We evaluated the population-level benefits of expanding treatment with the antiviral drug Paxlovid (nirmatrelvir/ritonavir) in the United States for SARS-CoV-2 Omicron variant infections. Using a multiscale mathematical model, we found that treating 20% of symptomatic case-patients with Paxlovid over a period of 300 days beginning in January 2022 resulted in life and cost savings. In a low-transmission scenario (effective reproduction number of 1.2), this approach could avert 0.28 million (95% CI 0.03–0.59 million) hospitalizations and save US $56.95 billion (95% CI US $2.62–$122.63 billion). In a higher transmission scenario (effective reproduction number of 3), the benefits increase, potentially preventing 0.85 million (95% CI 0.36–1.38 million) hospitalizations and saving US $170.17 billion (95% CI US $60.49–$286.14 billion). Our findings suggest that timely and widespread use of Paxlovid could be an effective and economical approach to mitigate the effects of COVID-19.


Estimating the within-host model parameters
We fix the initial number of viruses (V0) at 1/30 copy/mL (corresponding to a single viral particle per 30 mL of nasal wash in the upper respiratory tract (2)) and the initial number of target cells (U0) at 10 7 (1).For the Delta variant, the estimated average time from infection to symptom onset is 5 days (3); in recent clinical trials, the estimated average time from symptom onset to initiation of treatment is 3 days (4).Based on these estimations, we assume that treatment is initiated 8 days after infection for treated patients.
To estimate the five model parameters governing the viral load dynamics (i.e., the infection rate of susceptible cells [b], the rate at which infected cells die [𝛿𝛿], the rate at which active viruses were cleared [c], the virus production rate [p] and antiviral efficacy []), we fit the within-host model to the mean SARS-Cov-2 RNA titer (log10 copies/mL) at five time points (1, 3, 5, 10 and 14 days post initiation of treatment) measured across 1126 infected adults treated with a placebo during a clinical trial in late 2021 (4) and the mean SARS-Cov-2 RNA titer (log10 copies/mL) at five time points (1, 3, 5, 10 and 14 days post initiation of treatment) measured across 1120 infected adults who received Paxlovid in the same clinical trial (5).We set the initial viral load upon infection, V0, to correspond to one infectious virus particle in the upper respiratory tract (2).We assume that the average viral load at the initiation of treatment is 10 6 log10 copies/mL (4).We use the Stochastic Approximation Expectation-Maximization (SAEM) algorithm to estimate the five parameters (MONOLIX 2021R1) (6,7) and confirm the convergence of estimates via trace plots.

Modeling the daily infectiousness of treated and untreated cases
Our between-host SARS-CoV-2 transmission model assumes that the infectiousness of an infected individual depends on the number of days elapsed since they became infected ( ), whether or not they receive Paxlovid, and, if so, how quickly treatment is initiated.We use to indicate treatment initiation time in days after symptom onset and to denote that a case remains untreated.Specifically, we assume that an individual's infectiousness is proportional to: Where represents the individual's viral load t days after infection.We use the fitted within-host model above to generate the , depending on whether and when the infected individual receives Paxlovid and assuming that infectiousness drops to zero when the viral load drops below the detection threshold of 100 (8).

Between-host model of SARS-CoV-2 transmission and treatment with Paxlovidlike drug
Our between-host agent-based model assumes that an infected individual's daily infectiousness toward one of their contacts depends on: (i) the time elapsed since infection, (ii) whether and when Paxlovid treatment is initiated, and (iii) whether the case and contact live in the same household.We use the infectiousness equation above ( ) to account for the first two variables, and then solve for household and non-household scaling constants that yield target secondary infection rates.Specifically, we first calibrate the daily within-household transmission rates for untreated cases to match reported estimates for household secondary attack rates (which is constant across all scenarios).We then calibrate the daily non-household transmission rates for untreated cases so that the model produces a specified overall initial reproduction number (which depends on the scenario analyzed).
To calibrate the within-household transmission rate scaling constant ( ), we assume that a household secondary attack rate of 35% (9) and solve for the that satisfies .To calibrate the non-household transmission rate scaling constant ( ℎ ), we set the target initial effective reproduction number ( ) and then apply an interior point algorithm to find the value of that minimizes the mean square error between and the average initial across 100 simulated epidemics.For each simulation, we estimate   by calculating the average number of secondary infections across a random sample consisting of 1% of individuals infected during the first 100 days of the simulation.
At the start of a simulation, we set the proportions of the population with infectionacquired and vaccine-acquired immunity to values estimated from data provided by the U.S.
Centers for Disease Control and Prevention (Appendix Table 1).To estimate the number of previously vaccinated individuals and the date of their most recent dose, we simulated vaccination rates based on reported uptake in the U.S. from 2020 to 2022 (10).For each previously vaccinated individual, we randomly selected the date of their first dose (t1) based on the reported age-specific vaccine administration rates, starting on October 29, 2021 (11) for children between 5 and 11 years old, May 10, 2021 for children between 12 and 15 years old (12), and December 13, 2020 for all others.We then randomly determined whether and when an individual receives their second primary dose and first booster based on CDC-recommended waiting periods and reported rates of uptake.Specifically, we assumed second doses are administered beginning 3 weeks after the first dose, and the window for boosters depends on the timing of the booster dose, with a minimum gap of 8 months for individuals receiving their booster dose before September 23, 2021 (13), 6 months between September 24, 2021 and January 3, 2022 (14), and 5 months after January 4, 2022 (15).We initialized immunity in our simulations using the dates of the last dose received for each vaccinated individual (Appendix Table 1) (16).
For the previously infected individuals, we estimated their times of recovery.
Specifically, we collected the daily population proportion of confirmed cases in the USA from 2021 to 2022 from Our World In Data (10).For each individual infected previously at the start of the simulation, we estimated the date of the previous infection (tinfect) by taking draws from the distribution of the daily population proportion of cases between January 29, 2021 to January 29, 2022.We considered the time of recovery as (tinfect + 9), where 9 days is the average time lag between infection and recovery (17).
At the start of each simulation, we also assume that 1% of the unvaccinated susceptible and recovered populations are newly infected (exposed), which corresponds to ≈0.6% of the total population.We assumed age-stratified estimates for Paxlovid's efficacy at preventing hospitalizations (18) (Appendix Table 1) and incorporated uncertainty by sampling the Paxlovid efficacy parameters for each simulation from triangular distributions with mean, lower bound, and upper bound equal to the estimated mean, 95% CI lower bound, and 95% CI upper bound, respectively.To estimate therapeutic benefits of the drug via pairs of simulations, we enforced the same sequence of random numbers in each simulation.

Estimating the Years of Life Lost (YLL) Averted and Monetary Costs
For each set of stochastic simulations, we estimated the years of life loss (YLL) averted for each antiviral strategy  as follows: 1. Calculate the difference in incidence by age group as  , =  ,0 −  , , where  ,0 and  , are total deaths in age group a produced by the no treatment and strategy  simulations, respectively.
2. Estimate the YLL prevented by the strategy  as where   denotes the future-discounted life expectancy for individuals of age a.
Similarly, we determined the incremental monetary costs for each strategy  as given by where  0 and   are the total number of treatment courses administered in the no treatment and strategy  simulations, respectively,   is the price of administering one course of antivirals,  , and  0, are the total number of hospitalizations in age group a in each simulation, and  , is the median COVID-19 hospitalization cost for age group a.The cost parameter values are given in Appendix Table 3.
For a given willingness to pay for a YLL averted (), we calculated the net monetary benefit (NMB) of a strategy as We determined the optimal strategy across a range of scenarios, each defined by the effective reproduction number (  ), willingness to pay, and cost of a vaccine.

Appendix
The study provides estimates for adults over age 18y.We assumed that efficacy for children under 18 is the same as that for adults aged 18-49y.η: transition rate from treatment to hospitalized (d -1 ) 1/(5.9-1/γT) 5.9 d on average from symptomatic to hospitalized (29)   : transition rate from symptomatic to treatment (d  (33).which estimates   for boosters against Omicron and other studies that simultaneously estimate vaccine efficacy against infection, symptomatic infection, and mortality for the Pfizer-BioNTech BNT162b2 vaccine earlier in the pandemic.In Ref (34), vaccine efficacy against infection is estimated to be 64% when efficacy against symptomatic disease reaches 67% (21 d after vaccination).In Ref (35), vaccine efficacy against infection is estimated to be 42.8% when efficacy against symptomatic disease reaches 52.4% (14 d after the initial vaccine dose).In Ref (34), vaccine efficacy against infection is estimated to be 22% when efficacy against symptomatic disease reaches 44% (14 d after the initial vaccine dose).In Ref (36), vaccine efficacy against mortality is estimated to be 91.9% when efficacy against symptomatic disease reaches 66.3% (20 d after the second vaccine dose).
** Since direct estimates for   against the Omicron variant are not available, we extrapolated from Ref (37).which estimates   against Omicron and Ref ( 38), which reports that vaccine efficacy against symptomatic disease is 97% when efficacy against infection reaches 79% (14 d after the second vaccine dose).
Appendix Table 3 + Infectiousness is proportional log10 of viral load for values above 10 6 , as given by log10(Viral load)-6, and is set to zero otherwise (42).& Infectiousness is a constant for viral loads above 10 6 , and is set to zero otherwise (42).* Infectiousness has the sigmoid relationship with viral load following the association between viral load and cell culture isolation success rate (43).
Appendix Table 6

Public
Health Impact of Paxlovid as Treatment for COVID-19, United States Appendix Within-Host Model of SARS-CoV-2 Replication Dynamics The deterministic model given by    = −       =     −      = (1 − )  −   tracks the number of target cells at risk of infection (Ui), infected cells (Ii), and free viral particles (Vi) (1) (Appendix Figure 1).The rate at which free viral particles infect target cells is governed by the number of susceptible target cells, the number of free viral particles, and a fixed rate b.Viruses replicate at a rate p in infected cells; infected cells die at rate  and free viral particles die at rate c.The model assumes that Paxlovid inhibits the replication of viruses within infected cells, with efficacy .

Figure 1 .
Diagrams of the within-host and between-host models.(A) To estimate changes in infectivity following treatment with Paxlovid (T), we used a model that tracks the changing number of uninfected cells (U), infectious cells (I) and free viral particles (V) in an infected case, with and without treatment.(B) We projected population-level impacts of Paxlovid treatment using a stochastic individualbased model of SARS-CoV-2 transmission that considers age-specific risks and contact patterns in households, schools, workplaces, and other venues.Upon infection, susceptible (Su) and vaccinated (Sv) individuals progress to exposed (E), asymptomatic infectious (A) or presymptomatic (P) and then to either symptomatic infectious (Y) with (YT) or without (YU) Paxlovid treatment.A fraction of symptomatic caseswith or without treatment will be recovered (R) or hospitalized (H), and a subset of those will die (D).All asymptomatic cases eventually progress to a recovered class (R), where they remain protected from future infection.As immunity wanes, recovered individuals return to exposed (E) by reinfection.
(20)onstructed random links between individuals in different households based on reported age-specific contact rates in the U.S., stratified into age bins of 5-17, 18-49, 50-64, and over 65 years(20).Specifically, to determine the number of contacts a node in age group   has with nodes in age group   , we draw random deviates from Poisson distributions centered at the mean number of contacts between   and   .The resulting network includes 5000 households, 2019 nodes (people), and degrees (numbers of edges per node) that roughly follow a gamma distribution with shape and scale parameters of 3.69 and 3.41, respectively.We directly scaled our results to the 2019 U.S. population of 328 million (19)g the 129,697 households included in 2017 National Household Travel Survey(19).We assumed that households are fully connected (i.e., all nodes in the same household are linked by edges).

Table 2 .
Parameters governing waning of immunity following vaccination and infection with respect to the SARS-CoV-2 Omicron variant.Vaccine-related parameter values are based on estimates for the BNT162b2 (Pfizer) vaccine.Since direct estimates of   and   for vaccine booster doses against the Omicron variant are not available, we extrapolated from Ref *

Appendix Table 5. The optimal choice for Paxlovid treatment under a range of SARS-CoV-2 transmission scenarios. We
estimated the mean (95% confidence interval[CI]) of the number of cases infected averted (millions), number of deaths averted (thousands), number of hospitalizations averted (million), number of courses administered (millions), and net monetary benefit (NMB) in billions of USD, in contrast with baseline, which is scaled to a U.S. population of 328.2 million (21) (Appendix Table6).Each scenario V1-V3 changes one of the base assumptions, as indicated in the second column.Values in the third column are mean and 95% CI in the transmission scenarios (Re = 1.2 and Treatment rate = 20%) as examples.